### Photovoltaic Device Simulation

In semiconductor device simulation we attempt to solve the semiconductor equations using a computational method. Computational methods are necessary because to date no general analytical solution to these equations has been presented. Nevertheless, the advent of microprocessor technology has made it necessary for scientists to obtain such solutions. However, it is not only the micrprocessor industry that utilises semiconductor devices - the alternative energy industry ensures that the need to understand the inner workings of solar cells (photovoltaic devices) is a pressing one. It is difficult, and usually downright impossible, to make experimental observations of the physical processes governing the flow of charge inside a thin-film solar cell, simply because the cell is so thin (of the order of microns). If we can solve the semiconductor equations we can calculate the quantities of interest, and so gain some insight into the internal physics of the cell. This knowledge can assist in designing cells in an optimal way, which necessarily improves the technology. Careful simulation can be of great assistance to the experimentalist who wishes to fabricate cells since the simulation results can guide the experimentalist in his research. This is an important consideration for any laboratory, given the high costs involved in experimental scientific research.

Dr JSC Prentice has developed software for solving the above equations, using a multidimensional Newton-Raphson method based on a finite-difference approximation for the derivatives. This is a fairly standard approach, although other methods such as finite-element and Monte Carlo have been used in the field.

Naturally, the task of developing the software is only the first step in the process. Once it has been debugged, it is necessary to use the software for meaningful research.

The main thrust of Dr Prentice's research concerns the form of the optical generation rate *G(x)*. This is the rate of light (photon) absorption as a function of position within the thin-film solar cell. It is a fundamentally important quantity since the absorption of photons results in the creation of electron-hole pairs. These charged particles are accelerated by the electric fields present in the cell, which results in a current that flows through the cell (and any circuit in which the cell is located). Most of the photons that are absorbed by the cell are absorbed near the front surface, with relatively fewer being absorbed near the back of the cell. The quantity *G(x)* therefore decreases in magnitude from the front to the back of the cell.

The *form* of *G(x) *refers to this positional variation in *G(x)*. We cannot easily control the form of *G(x)* in the laboratory (which hinders experimental research in this particular area), but from a simulation point of view it is easy to adjust *G(x)*. The idea is to solve the semiconductor equations for various forms of *G(x)* and to study the variation in the power output of the cell. We have already observed that the power output of an amorphous silicon-based cell varies considerably as the form of *G(x)* is changed, and there does seem to be an optimal form of *G(x)* for this particular cell. The output of the simulation allows us to make a detailed study of why there should be an optimum at all, and of the way in which charge distributions and electric fields inside the cell change when the form of *G(x)* is changed.

Of course, the capacity to calculate *G(x)* is paramount in this sort of research (note that *G(x)* is an input for the simulation, not an output). To this end, Dr Prentice has developed two simple models for calculating *G(x)* in any absorbing layer of a multilayer structure. It is necessary to consider a multilayer structure because solar cells are typically composed of several layers, some of which may be transparent. The various multiple internal reflections that occur inside each layer can affect *G(x)* in a given layer, and so these multiple internal reflections must be taken into account. The two models are capable of doing this.

They are based on a multiple matrix method, and consider the optical constants of each layer. These constants determine the reflection at the interface between adjacent layers and the absorption within a layer. One of the models is a photon-based model which calculates *G(x)* by assuming that the incident light is composed of a stream of photons. The other model assumes the light has a wave-nature and takes into account phase differences between waves at every position in the multilayer structure. Such a model is termed a coherence model. The coherence model has also been adapted to cater for so-called partial coherence, in which the phase differences between waves are affected by variations in the thicknesses of the layers. Under extreme conditions of variations in layer thicknesses the coherence model is equivalent to the photon model.